I've made such a mess of things, I'm about to cry...

You see, I have two hard disks on my computer: C, which is called System, and D, which is called Data.

Everything goes straight to C, and it was getting filled completely, so I thought I'd move my Sims 3 to the empty D.
But I did it manually (clip and paste with the mouse), and something didn't work.

Then I thought, that I could just delete everything and re-install, starting with the sims 3 base game.

It won't let me. It claims that there is a version already installed, and that I must first remove it, if I wish to install.

I can't find the old version anywhere on hard disks C or D.

If I go to the control panel and pick remove program, sims stuff does appear, but when I then start removal, it tells me that it isn't at that location any more.
It's like it is telling me to remove something that isn't there, and until I do, I can't install anew.

Is there any way anyone can help me?

Follow these instructions - Game Help:TS3 Uninstall^wiki. Jump straight to the section "1.2.4 Cleaning up the Registry".

Thank you so much, but sadly it didn't help. I did apparently have some registry issues which are now fixed, but they seem to not be the problem.

It says:

The installation program has registered that version 1.29.055 of The Sims 3 is already installed.

This installation program installs an earlier version (1.0.631).

You must uninstall the earlier version, before installing this version.

When I go to the Control Panel, there is still a list of sims games, and when I press remove, I get an error message, with this being the reason (fejlkode means error code, fejlinformation means error information):

Fejlkode: -5005 : 0x80070002
Fejlinformation:
>Kernel\KernelMedia.cpp (95)
>SetupNew\setup.cpp (851)
PAPP:
PVENDOR:Electronic Arts (http://www.TheSims3.com)
PGUID:C05D8CDB-417D-4335-A38C-A0659EDFD6B8
$15.0.0.498
@Windows Vista Service Pack 2 (6002)
IE Version: 9.0.8112.16421

You haven't deleted everything, in that case - there are either files or (more likely) registry entries left. If ccleaner didn't finish the job, do it manually, paying attention to the "backup" stage.

I think I broke my feeble brain, but it finally worked.
Let me tell you, tinkering in there scared me, even though I did make the backup.

I'm so incredibly grateful for your help! (Should you need someone beaten up, or some *ahem* favour performed, you may call on me - I think I love you.)